Calculus Examples

${(\frac{4}{3})}^{3} - 4 {(\frac{4}{3})}^{2} - 3 (\frac{4}{3}) + 5$

Step 1

Simplify each term.

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Step 1.1

Apply the product rule to $\frac{4}{3}$ .

$\frac{4^{3}}{3^{3}} - 4 {(\frac{4}{3})}^{2} - 3 (\frac{4}{3}) + 5$

Step 1.2

Raise $4$ to the power of $3$ .

$\frac{64}{3^{3}} - 4 {(\frac{4}{3})}^{2} - 3 (\frac{4}{3}) + 5$

Step 1.3

Raise $3$ to the power of $3$ .

$\frac{64}{27} - 4 {(\frac{4}{3})}^{2} - 3 (\frac{4}{3}) + 5$

Step 1.4

Apply the product rule to $\frac{4}{3}$ .

$\frac{64}{27} - 4 \frac{4^{2}}{3^{2}} - 3 (\frac{4}{3}) + 5$

Step 1.5

Raise $4$ to the power of $2$ .

$\frac{64}{27} - 4 \frac{16}{3^{2}} - 3 (\frac{4}{3}) + 5$

Step 1.6

Raise $3$ to the power of $2$ .

$\frac{64}{27} - 4 (\frac{16}{9}) - 3 (\frac{4}{3}) + 5$

Step 1.7

Multiply $- 4 (\frac{16}{9})$ .

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Step 1.7.1

Combine $- 4$ and $\frac{16}{9}$ .

$\frac{64}{27} + \frac{- 4 \cdot 16}{9} - 3 (\frac{4}{3}) + 5$

Step 1.7.2

Multiply $- 4$ by $16$ .

$\frac{64}{27} + \frac{- 64}{9} - 3 (\frac{4}{3}) + 5$

Step 1.8

Move the negative in front of the fraction.

$\frac{64}{27} - \frac{64}{9} - 3 (\frac{4}{3}) + 5$

Step 1.9

Cancel the common factor of $3$ .

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Step 1.9.1

Factor $3$ out of $- 3$ .

$\frac{64}{27} - \frac{64}{9} + 3 (- 1) \frac{4}{3} + 5$

Step 1.9.2

Cancel the common factor.

$\frac{64}{27} - \frac{64}{9} + 3 \cdot - 1 \frac{4}{3} + 5$

Step 1.9.3

Rewrite the expression.

$\frac{64}{27} - \frac{64}{9} - 1 \cdot 4 + 5$

Step 1.10

Multiply $- 1$ by $4$ .

$\frac{64}{27} - \frac{64}{9} - 4 + 5$

Step 2

Find the common denominator.

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Step 2.1

Multiply $\frac{64}{9}$ by $\frac{3}{3}$ .

$\frac{64}{27} - (\frac{64}{9} \cdot \frac{3}{3}) - 4 + 5$

Step 2.2

Multiply $\frac{64}{9}$ by $\frac{3}{3}$ .

$\frac{64}{27} - \frac{64 \cdot 3}{9 \cdot 3} - 4 + 5$

Step 2.3

Write $- 4$ as a fraction with denominator $1$ .

$\frac{64}{27} - \frac{64 \cdot 3}{9 \cdot 3} + \frac{- 4}{1} + 5$

Step 2.4

Multiply $\frac{- 4}{1}$ by $\frac{27}{27}$ .

$\frac{64}{27} - \frac{64 \cdot 3}{9 \cdot 3} + \frac{- 4}{1} \cdot \frac{27}{27} + 5$

Step 2.5

Multiply $\frac{- 4}{1}$ by $\frac{27}{27}$ .

$\frac{64}{27} - \frac{64 \cdot 3}{9 \cdot 3} + \frac{- 4 \cdot 27}{27} + 5$

Step 2.6

Write $5$ as a fraction with denominator $1$ .

$\frac{64}{27} - \frac{64 \cdot 3}{9 \cdot 3} + \frac{- 4 \cdot 27}{27} + \frac{5}{1}$

Step 2.7

Multiply $\frac{5}{1}$ by $\frac{27}{27}$ .

$\frac{64}{27} - \frac{64 \cdot 3}{9 \cdot 3} + \frac{- 4 \cdot 27}{27} + \frac{5}{1} \cdot \frac{27}{27}$

Step 2.8

Multiply $\frac{5}{1}$ by $\frac{27}{27}$ .

$\frac{64}{27} - \frac{64 \cdot 3}{9 \cdot 3} + \frac{- 4 \cdot 27}{27} + \frac{5 \cdot 27}{27}$

Step 2.9

Reorder the factors of $9 \cdot 3$ .

$\frac{64}{27} - \frac{64 \cdot 3}{3 \cdot 9} + \frac{- 4 \cdot 27}{27} + \frac{5 \cdot 27}{27}$

Step 2.10

Multiply $3$ by $9$ .

$\frac{64}{27} - \frac{64 \cdot 3}{27} + \frac{- 4 \cdot 27}{27} + \frac{5 \cdot 27}{27}$

Step 3

Combine the numerators over the common denominator.

$\frac{64 - 64 \cdot 3 - 4 \cdot 27 + 5 \cdot 27}{27}$

Step 4

Simplify each term.

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Step 4.1

Multiply $- 64$ by $3$ .

$\frac{64 - 192 - 4 \cdot 27 + 5 \cdot 27}{27}$

Step 4.2

Multiply $- 4$ by $27$ .

$\frac{64 - 192 - 108 + 5 \cdot 27}{27}$

Step 4.3

Multiply $5$ by $27$ .

$\frac{64 - 192 - 108 + 135}{27}$

Step 5

Simplify the expression.

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Step 5.1

Subtract $192$ from $64$ .

$\frac{- 128 - 108 + 135}{27}$

Step 5.2

Subtract $108$ from $- 128$ .

$\frac{- 236 + 135}{27}$

Step 5.3

Add $- 236$ and $135$ .

$\frac{- 101}{27}$

Step 5.4

Move the negative in front of the fraction.

$- \frac{101}{27}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$- \frac{101}{27}$

Decimal Form:

$- 3.\overline{740}$

Mixed Number Form:

$- 3 \frac{20}{27}$